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First principles study of the crystal, electronic structure, and diffusion mechanism of polaronNa vacancy of Na3MnPO4CO3 for Na-ion battery applications

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2017 J. Phys. D: Appl. Phys. 50 045502
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Journal of Physics D: Applied Physics
J. Phys. D: Appl. Phys. 50 (2017) 045502 (6pp)

doi:10.1088/1361-6463/aa518d

First principles study of the crystal,

diffusion mechanism of Na ions in Na3MnPO4CO3 using density functional theory with a
Hubbard potential correction. Our results suggest that the structure of Na3MnPO4CO3 can be
deintercalated with more than one Na ion, and that the removal of a Na ion can form a bound
polaron. We find that our calculations of the intercalation voltages for the redox couples
Mn2+ /Mn3+ and Mn3+ /Mn4+ agree very well with the experimental data. In addition, we
demonstrate that Na in Na3MnPO4CO3 can diffuse in three directions with low activation
energy barriers, allowing a fast charging rate.
Keywords: DFT method, battery, neb method, Bader population
(Some figures may appear in colour only in the online journal)

1. Introduction

energy, safety etc). Owing to their remarkable electrochem­
ical and thermal properties, and their flexibility to increase the
open-circuit voltage, transition metal compounds containing
different polyanion units [1, 2] are considered as the most
promising cathode materials for the next generation of Li-ion
batteries. Among this class, carbonophosphate mat­erials
with the general formula Li3MCO3PO4(M  =  Fe, Mn, Co,
V) reported for the first time in 2011 by Hautier et al [3] are

Lithium ion batteries are well known as a popular power
source with many applications in our daily life. Despite this
success, the improvement of the energy storage capacity of
this technology is a challenge. To improve the overall bat­
tery performance, it is necessary to explore new cathode mat­
erials with better characteristics (capacity, voltage, specific
1361-6463/17/045502+6$33.00

1

Na(1)
4f
0.7421
0.9982
0.7526
They also have the potential to maintain the safety charac­
Na(2)
2e
0.0838
0.2500
0.7572
teristics of olivine [5]. In particular, the Mn-based materials
C
2e
0.0611
0.7500
0.7389
display a specific energy 45% greater that of LiFePO4, but so
O(1)
2e
0.1207
0.7500
0.9649
far only  ∼135 mAh g−1 has been obtained experimentally.
O(2)
2e
0.1464
0.7500
0.5382
In addition, they are able to keep a stable structure upon the

Among the most used compounds, Mn-based carbonophos­ in our calculations and all the structures were relaxed until the
phate materials represent the most stable chemical class [15] energy and the forces were converged to less than 10−6 eV and
˚ −1 respectively. The Brillouin zones were sampled
and demonstrate a good reversibility of Na intercalation and 10−3 eV A
deintercalation [7, 16]. Recently, Chang et al [16] have dem­ with a 8 × 6 × 6 Monkhorst–Pack [22] grid to ensure geo­
onstrated that a compound with the sidorenkite structure metrical and energetic convergence. The average intercalation
(Na3MnPO4CO3) could play an important role in Na-ion bat­ voltage Vavg was calculated by using the already developed
teries due to its good cyclability, high average voltage (∼ 4V ) methods [23, 24] with Vavg = −∆E /F , where F is the Faraday
and its high capacity (∼125 mAh g−1: 66% of the theoretical constant and ∆E is the internal energy calculated as:
value), which is super­ior to most oxide cathode materials 
[10, 18]. In addition to that, it is able to deliver two-electron ∆E = E tot (Na3MnPO4CO3) − E tot (Na2MnPO4CO3) − E tot (Na),
(1)
transfer reactions per formula via electrochemically active
Mn2+ /Mn3+ and Mn3+ /Mn4+ redox reactions. These results and

were recently confirmed by experimental studies [16, 19], ∆E = E tot (Na2MnPO4CO3) − E tot (NaMnPO4CO3) − E tot (Na),
which demonstrate for the first time that this material exhibits
(2)
a high specific capacity of 176.7 mAh g−1, reaching 92.5% where Etot(Na) is the total energy for metallic sodium in a
of its theoretical value (191 mAh g−1). These findings dem­ body-centered-cubic (bcc) crystal structure. The activation
onstrate the potential of this material as a very good cathode barriers were calculated using the nudged elastic band (NEB)
material for the future. In spite of this, the electronic structure method [25] and a 1 × 2 × 2 supercell. Finally, Bader popula­
and the electrochemical properties of this compound have not tion analysis was used to determine the atomic charges with a
been sufficiently investigated.
300 × 200 × 200 grid for the electron density.
Here, using DFT calculations, we report the electronic
structure and magnetic properties of Na3MnPO4CO3 before
and after the removal of Na ions. Also, we show how a bound 3.  Results and discussion
polaron is formed when the defect has been created, and then
Three


Na2MnPO4CO3
NaMnPO4CO3

Exp. [16]
Exp. [16]
Exp. [7]
Exp. [26]
AFM
AFM
FM

a

b

c

α

β

γ

V

Sym.

m(Mn)


91.78

90.12
89.70
90.13
90.10
89.9
88.013
88.59

90
90
90
90
90
90
87.82

312.32
310.74
312.78
313.13
315.1
311.4
298.7

P21/m
P21/m
P21/m
P21/m

the magnetic ground state of each compound is shown. For
Na3MnPO4CO3, the calculated lattice parameters a and c are
slightly overestimated compared to the parameters of natural
sidorenkite, by about  ∼1.3%, but basically in agreement with

those of synthetic sidorenkite as reported by Chen et al [16].
After removing the alkali atoms, we found that the resulting
volume change is about −1% and −4% for Na2MnPO4CO3
and NaMnPO4CO3 respectively. For the latter, the angles
between the lattice vectors are changed after removing two
Na ions, inducing a symmetry change from monoclinic to tri­
clinic. In addition to the geometrical optimization, we have
also calculated the total energy difference between the FM
and AFM configurations of Na3MnPO4CO3. We found that the
difference is very small, with ΔEFM–AFM  =  3.49 meV, which
means that the FM and AFM ordering are in competition.
When the alkali cation are removed, we found that the magn­
etic moment of Mn is decreased by  ∼17% and  ∼18% for the
Na3MnPO4CO3 and Na2MnPO4CO3 compounds respectively.
The decrease of the magnetic moment indicates that the trans­
ition metal exists in two spin states. This is confirmed by the
experimental finding, which shows that Mn exists in two dif­
ferent states at each step.
3


M Debbichi et al

J. Phys. D: Appl. Phys. 50 (2017) 045502


−1.82
−1.81

+0.89/+  0.89
+2.14
+4.85
+3.93
−1.64
−1.81
−1.89
1.73
−1.81
−1.71

Redox couple

+0.90/+  90
+3.03
+4.86
+3.94
−1.70
−1.61
−1.89
−1.70
−1.71
−1.64

2+

3+

and  ∼0.21 V for Mn3+ /Mn4+ . Due to the inductive effect (the
increase in voltage from the oxide voltage) [16], the obtained
voltage of the redox couples are slightly higher with respect to
most known oxide cathode materials [10, 28].
Since the mobility of the alkali atoms in the electrode
compound is a key aspect of the rate capability of recharge­
able batteries, the determination of the activation barriers for
the migration of the Na ion in the material is essential. As
shown in the previous paragraph, the removal of a Na ion from
Na3MnPO4CO3 results in the oxidization of Mn2+ to Mn3+ .
In addition, we found that the average Mn3+ –O bond is short­
ened by  ∼0.13 Å compared with that of the Mn2+ –O bond,
which caused the lattice distortion of the Na23(MnPO4CO3)8.
This effect is in fact a sign of the presence of a small polaron
at the Mn3+ site. As pointed out by Dinh et al [14, 29], when
the Na vacancy moves, the bound polaron at the transition
metal site consequently migrates. To describe the migration
pathway of the polaron, the Na diffusion path was calculated
and is presented in figure 2 with a green color. We found that
the diffusion can occur inside a double layer (intrablock) and
between two adjacent double layers (interblock) as shown in
figures 2(a) and (b) (demonstrated by the highlighted Na ions
and their connected lines). For the intrablock diffusion, three
possible elementary diffusion processes (EDP) have been
considered and called: Na2-Na14, Na2-Na16 and Na2-Na22.
However for the interblock diffusion we only considered the
most preferable EDP called N2-N12.
The couple of Na vacancies with its accompanying
polaron are shown in figure 2(a) and are indexed as Na2-Mn8,
Na12-Mn2, Na14-Mn6 and Na22-Mn8. The activation energy

ition from Na3MnPO4CO3 to Na2MnPO4CO3, the unoccupied
states located at about 5 eV are split into two different groups.
Consequently, the peak at 1 eV in the partial density (PDOS)
of Mn in Na2MnPO4CO3 has totally disappeared in the corre­
sponding Mn-PDOS of Na3MnPO4CO3, which indicates an
important charge reorganization. From Na2MnPO4CO3 to
NaMnPO4CO3, we found the presence of some new spin states
in the vicinity of 1 eV, due to the strong hybridization between
O and Mn atoms. This is related to the presence of vacancies
leading to the oxidization of manganese from Mn3+ to Mn4+ .
These results confirm the two-stage redox reaction mech­
anism as proposed in [16]. The charge reorganization also
affects the PDOS of the other elements for Na2MnPO4CO3
and NaMnPO4CO3 by shifting toward higher energies. This is
due to a modified hybridization with the Mn ion.
To gain more information about the charge distribution in
the different systems, the Bader charges were calculated and
are shown in table 3. Upon the desintercalation of the Na ions,
we found that the charge of the Mn atom is changed signifi­
cantly compared to the others elements. From Na3MnPO4CO3
to Na2MnPO4CO3 the Mn charge increases from  
+1.47
to  +2.14, while in NaMnPO4CO3 it has a charge of  +3.03.
4


M Debbichi et al

J. Phys. D: Appl. Phys. 50 (2017) 045502


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comparable activation barriers—meaning that the change of
the magnetic element does not significantly alter the diffusion
of the Na ions.
For the interblock diffusion (called P3), as shown in
figure 2(b), the Na2 vacancy intends to move to the left side
to occupy Na12, while the polaron jumps from the Ma8 to
the Mn2 site and the activation energy of this path is 0.85 eV.
By combining these preferential elementary processes, we
conclude that the diffusion of Na can occur in 3 dimen­
sions: along the [1 0 0] direction with an Ea = 0.85 eV, in the
[0 1 0] direction with Ea = 0.56 eV and in the [0 0 1] direc­
tion through the double carbon layer with Ea = 0.64 eV. These
5


M Debbichi et al

J. Phys. D: Appl. Phys. 50 (2017) 045502

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